Volume of a Cylinder Examples in Math

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Volume of a Cylinder.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.

Concept Recap

The amount of three-dimensional space inside a cylinder, found by multiplying the area of the circular base by the height.

Imagine stacking hundreds of identical circular coins into a tall tower. Each coin is a thin circle with area πr2\pi r^2, and stacking hh units high gives you a cylinder. The volume is just the area of one coin times the height of the stack.

Read the full concept explanation →

How to Use These Examples

  • Read the first worked example with the solution open so the structure is clear.
  • Try the practice problems before revealing each solution.
  • Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Cylinder volume is base area repeated through height.

Common stuck point: The procedure for volume of a cylinder is the easy part; the trap is using 2πr2\pi r instead of πr2\pi r^2 for the base. Asking "Can I identify the circular base area and the height?" first is what keeps a correct-looking calculation from being attached to the wrong concept.

Sense of Study hint: Ask: Can I identify the circular base area and the height?

Worked Examples

Example 1

easy
A cylinder has a radius of 4 cm and a height of 10 cm. Find its volume. Use π≈3.14\pi \approx 3.14.

Answer

V=160π≈502.4V = 160\pi \approx 502.4 cm³.

First step

1
Step 1: Write the formula for the volume of a cylinder: V=πr2hV = \pi r^2 h.

Full solution

  1. 2
    Step 2: Substitute the values: V=π×42×10=π×16×10=160πV = \pi \times 4^2 \times 10 = \pi \times 16 \times 10 = 160\pi.
  2. 3
    Step 3: Approximate: V≈160×3.14=502.4V \approx 160 \times 3.14 = 502.4 cm³.
The volume of a cylinder is the area of the circular base (πr2\pi r^2) multiplied by the height (hh). This formula makes intuitive sense: you are stacking up infinitely many thin circular disks of area πr2\pi r^2 to a total height hh.

Example 2

medium
A cylindrical water tank holds 2000π2000\pi liters. Its height is 20 m. Find the radius of the tank.

Example 3

medium
A cylindrical mug has diameter 88 cm and height 1010 cm. How many cm³ does it hold (use π≈3.14\pi\approx 3.14)?

Example 4

medium
A cylinder has radius 44 and height hh. Its volume equals 80π80\pi. Find hh.

Example 5

medium
Water in a cylinder of radius 33 has depth 88. The water is poured into an empty cylinder of radius 44. Find the new depth.

Example 6

hard
A hollow cylindrical pipe has outer radius 55, inner radius 44, and length 2020. Find the volume of material.

Example 7

hard
A rectangle with sides 66 and 1010 is rolled into a cylinder by joining the two sides of length 1010. Find the volume of the resulting cylinder (no top or bottom).

Example 8

challenge
A cylinder is inscribed in a sphere of radius 55 with the cylinder's axis through the sphere's center. Find the height that maximizes volume, and give that volume in terms of π\pi.

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

easy
A soup can has a diameter of 8 cm and a height of 12 cm. Find the volume. Leave your answer in terms of π\pi.

Example 2

hard
Two cylinders have the same volume. Cylinder A has radius 3 and height 16. Cylinder B has height 4. Find the radius of Cylinder B.

Example 3

easy
A cylinder has radius 55 and height 66. Find its volume in terms of π\pi.

Example 4

easy
A cylinder has diameter 1010 and height 77. Find its volume in terms of π\pi.

Example 5

easy
Find the volume of a cylinder with radius 22 cm and height 1111 cm. Use π≈3.14\pi\approx 3.14.

Example 6

medium
A cylinder has volume 98π98\pi and radius 77. Find its height.

Example 7

medium
A cylinder has volume 108π108\pi and height 33. Find its radius.

Example 8

medium
A water bottle is a cylinder with radius 33 cm and height 2020 cm. How many milliliters does it hold? (1 cm3=1 mL1\text{ cm}^3=1\text{ mL}, use π≈3.14\pi\approx 3.14.)

Example 9

medium
A pool is a cylinder with radius 55 m and depth 22 m. How many cubic meters of water does it hold? Leave answer in terms of π\pi.

Example 10

medium
A cylinder of radius 44 and height 99 is melted and recast into a cylinder of radius 66. Find the new height.

Example 11

hard
A cylindrical silo has volume 1000π1000\pi m³ and height 1010 m. Find its diameter.

Example 12

hard
A cylindrical tank of radius 22 m is being filled at 4π4\pi m³/min. How fast (in m/min) does the water level rise?

Example 13

hard
Two cylinders have equal volumes. Cylinder A has radius 44 and height 99. Cylinder B has radius 66. Find Cylinder B's height.
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Background Knowledge

These ideas may be useful before you work through the harder examples.

area of circlevolume